Linear transformations and matrices Math 130 Linear Algebra
... We’ve already discussed isomorphisms. An isomorphism T : V → W is a linear transfor' mation which is also a bijection; its inverse function T −1 : W → V is also an isomorphism. Properties of linear transformations. A few important properties follow directly from the definition. For instance, every l ...
... We’ve already discussed isomorphisms. An isomorphism T : V → W is a linear transfor' mation which is also a bijection; its inverse function T −1 : W → V is also an isomorphism. Properties of linear transformations. A few important properties follow directly from the definition. For instance, every l ...
2/4/15
... the map Z → V ⊗ W is straightforward.3 Thus we see that we could alternately define V ⊗ W as the vector space with basis vi ⊗ wj . From this it follows that dim V ⊗ W = mn. Important: the vector space V ⊗ W is spanned by vectors of the form v ⊗ w, but not every vector in V ⊗ W can be written in this ...
... the map Z → V ⊗ W is straightforward.3 Thus we see that we could alternately define V ⊗ W as the vector space with basis vi ⊗ wj . From this it follows that dim V ⊗ W = mn. Important: the vector space V ⊗ W is spanned by vectors of the form v ⊗ w, but not every vector in V ⊗ W can be written in this ...
LECTURE NOTES CHAPTER 2 File
... • Vector: parameter possessing magnitude and direction which add according to the parallelogram law. Examples: displacements, velocities, accelerations. • Scalar: parameter possessing magnitude but not direction. Examples: mass, volume, temperature ...
... • Vector: parameter possessing magnitude and direction which add according to the parallelogram law. Examples: displacements, velocities, accelerations. • Scalar: parameter possessing magnitude but not direction. Examples: mass, volume, temperature ...
Unit 5 Notes
... The center of mass of an object is the part of an object that would move in the same way as a particle would if subjected to the same net force. In other words, if we had a uniform 2m long pipe, the center of mass would be at the 1m mark. If we had a 1m diameter uniform circle made from plywood, th ...
... The center of mass of an object is the part of an object that would move in the same way as a particle would if subjected to the same net force. In other words, if we had a uniform 2m long pipe, the center of mass would be at the 1m mark. If we had a 1m diameter uniform circle made from plywood, th ...